Doctorat Lmd en Mathématique
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Item Systèmes elliptiques quasi-linéaires avec dépendances du gradient et potentiel de Hardy-Leray singulier(University of Tlemcen, 2025-04-22) Kazi Tanii-Bougherara, AsmaCette thèse propose une approche innovante pour résoudre des systèmes d'EDP non linéaires elliptiques avec des termes dépendant du gradient et/ou du potentiel. Un nouveau schéma itératif est proposé dans les espaces de Lebesgue pondérés par le biais des inégalités de Hardy et de Caffarelli-Kohn-Nirenberg. Une courbe optimale est présentée pour distinguer les zones d'existence et de non-existence selon les paramètres p et q. Des sur-solutions radiales explicites sont également construites pour des domaines bornés.Item Sur les perturbations singulières dans les inclusions différentielles - Sur la compétition dans le chémostat avec inhibiteur externe(University of Tlemcen, 2019-02-27) Bar, BachirCette Thèse a un double objectif, l’un est l’étude des perturbations des inclusions différentielles par la méthode des échelles multiples, l’autre est l’étude d’un modèle de chemostat avec inhibition. La première est considérée quand on a un système singulièrement perturbé des inclusions différentielles , où une application pour un système ressource-consommateur est considérée, et lorsque nous avons une inclusion différentielle avec maximum, où la méthode de la moyennisation est utilisée pour étudier la limite des solutions. La seconde est l’étude d’un modèle de chemostat avec inhibiteur externe, où nous analysons les équilibres du système et construisons le diagramme opératoire.Item Contribution à l’analyse des problèmes elliptiques fractionnaires avec des nonlinéarités discontinues(University of Tlemcen, 2023-06-25) Achour, HanaaDans cette thèse, nous étudions une classe de problèmes elliptiques fractionnaires impliquant un second membre qui varie en terme singulier de diffusion, d’absorption ou d’une discontinuité nonlinéaire qui change de signe et aussi dans le cas où ce second membre est une combinaison de ces termes précédents, sous différentes hypothèses, nous obtenons les résultats d’existence et de multiplicité en utilisant des méthodes variationnelles, la théorie du point critique et une technique d’approximation.Item ETUDE DE CERTAINS PROBLEMES NON LOCAUX AVEC PERTE DE COMPACITE.(University of Tlemcen, 2023-09-18) Senhadji, AsmaItem Etude datamining de la stabilité, formabilité et les propriétés mécaniques des fluoropérovskités de type ABF3(University of Tlemcen, 2023-06-26) Belabbas, ZhourItem Mathematical models in ecology: case of density-dependent mortality rates(University of Tlemcen, 2023-12-04) Hammoum, AminaItem Modélisation de la croissance tumorale et interaction avec le système immunitaire(University of Tlemcen, 2023-10-25) Kaid, ZinebItem Sur un modèle épidémiologique structuré en âge Stabilité et Contrôle Optimal(University of Tlemcen, 2023-07-17) Bouayad Agha Née Sari, ZakyaItem Etude des Théorèmes limites sous des conditions de dépendance faible.(University of tlemcen, 2022-12-03) Bernou, IsmahenIn this thesis, we are interested in the asymptotic behavior of a class of stochastic processes with d-Φ-subgaussian increments and weighted sums of random variables with infinite means. For the first family of processes, the Dudley metric entropy criterion is used to establish a law of iterated logarithm. For the second family, a weak law of large numbers is proved in a unified framework under weak dependence conditions. A necessary condition for the validity of this law is also derivedItem Etude de l’influence des facteurs de croissance sur un mod`ele math´ematique de la Leuc´emie my´elo¨ıde chronique(university of tlemcen, 2022-11-15) Derrar Née Elouchdi, Fatima ZohraA partir des r´esultats obtenus dans ce travail, nous envisageons d’´etudier la bifurca- ` tion de Hopf et de v´erifier si ´eventuellement notre syst`eme est chaotique. Une discr´etisation du mod`ele nous permetterait de v´erifier les r´esultats obtenus `a partir de simulations num´eriques, et d’´etudier la stabilit´e globale dans le cas du sc´enaro 2 qui n’a pas ´et´e possible par les m´ethodes connues, car la solution n’est pas born´ee. En perspectives, il serait int´eressant d’´etudier le comportement asymptotique de mod`eles structur´es en ˆages( un tel mod`ele nous donnerait une meilleure pr´ecision ) ou de mod`eles contenant des ´equations aux d´eriv´ees partielles et des ´equations diff´erentielles ordinaires. Il est question aussi de trouver des mod`eles tenant en compte des cellules qui´escentes et des m´ecanismes mol´eculaires. Nous voudrions aussi v´erifier si l’injection de contrˆoles hybrides dans notre mod`ele, pourrait ,th´eoriquement,booster les cellules saines tout en diminuant la prolif´eration des cellules canc´ereuses. Le probl`eme de contrˆole se basera sur l’existence et l’unicit´e d’un contrˆole optimal. Une autre perspective serait l’introduction d’un param`etre de retard qui prendrait en compte le temps ´ecoul´e entre le d´eclenchement de la LMC et l’entr´ee en ligne des facteurs de croissance qui activent le syst`eme immunitaire. Il est pr´evu aussi d’´etudier des mod`eles tenant en compte des contrˆoles mod`elisant une chimioth´erapie et/ou immunot´erapie.Item Problèmes d’estimation dans les processus AR aléatoires.(University of Tlemcen, 2022-06-09) Boukhiar, SouadWe consider the class of resolvent estimators of the correlation operator ruling the functional autoregressive processes introduced by Mas. Under mild conditions on smoothing parameter, we establish exponential bounds and almost sure convergence of the resolvent estimators as well as convergence rates improving the existing results. As a consequence we derive asymptotic results on the resolvent predictors. Thereafter, we address the class of Hilbert space valued autoregressive process with random coefficients (RCARH). We derive limit theorems : strong law of great numbers, central limit theorem, compact law of the iterated logarithm and exponential inequalities and also we obtain rates of convergence. These results are crucial in the framework of Hilbert space autoregressive processes statistical analysis. We deal with resolvent estimators of the mean of random operators ruling a functional autoregressive process equation. Under mild conditions on the decay rate of a regularizing parameter, we obtain convergence in probability, exponential bounds, almost sure convergence and limiting law of the estimators and as well as results on resolvent predictors. These estimators achieve parametric rate p n (up to a logn factor). An estimator of the term variance of random operators is proposed and its convergence in probability is also shown. All these results extend and improve those of Mas in the framework of functional AR Processes with deterministic coefficients. Numerical studies and real data simulation’s are performed and adequately validate the efficiency of the resolvent predictors for Hilbertian deterministic autoregressive and random coefficient autoregressive iv Abstract models. The performance of the statistical predictor is measured by the errors forcasting and is compared to other methods existing in the literature showing competitive results.Item Sur certains modèles mathématiques en biologie et médecine.(University of Tlemcen, 2022-06-09) Zettam, Manel YousraThe main objective of this thesis is to analyze two mathematical models that describes the dynamics of cellular population in the case of chronic myeloid leukemia disease. To answer this biological problem, our work was devided into two parts : In the first part, we started with an quantitative and qualitative study for an hybrid mathematical model ([51]) that describes the dynamics of hematopoietic stem cell population in the chronic myeloid leukemia disease. First, we formulate the basic model as a one which contain two equations, one of them represent an age structured equation and the other one is an ordinary differential equation. Next to understand behaviour of our solutions we study the existence of steady state and their stability. In the second part, we studied the existence of steady states and their stability for an age structured model of leukemic diseases wich has developped by the authors ([13], [3]) in the case that the normal and leukemic stem cells proliferate from the ages a1 and a2 respectively. Then we transforme the (PDE) system to an (ODE) system in the case that the division rates and the death rates of normal stem cells and leukemia cells are constant.Item Variétés de contacts complexes.(university of tlemcen, 2021-06-23) Kadi, Fatima ZohraOur objective was to study the symmetry properties of complex contact manifolds. We started by studying the symmetry properties of normal complex contact manifolds, namely, Ricci-symmetry, Ricci-semi-symmetry and Ricci-pseudo-symmetry. The results obtained : 1. A normal complex contact manifold is Ricci-semi-symmetric if and only if it is an Einstein manifold. 2. A complex contact space form with constant GH-sectional curvature c is est properly Ricci-pseudo-symmetric (Lρ 6= 0) if and only if c = −1. 3. The non-existence of properly pseudo-symmetric (LR 6= 0) complex contact space form. In addition, the symmetry properties of complex (κ, µ)-spaces have been studied and it has been shown that 1. The complex (κ, µ)-spaces (κ < 1) are not Einstein. 2. The complex (κ, µ)-spaces (κ < 1) are Ricci-symmetric, Ricci-semi-symmetric if and only if they are locally isometric to C n+1 × CP n(16). 3. The complex (κ, µ)-spaces (κ < 1) are not properly Ricci-pseudo-symmetric. 4. The space C n+1 × CP n(16) is locally symmetric.Item Modélisation et étude mathématique de la propagation d’une maladie vectorielle (paludisme) au sein d’une population.(University of Tlemcen, 2021-12-16) Yacheur, SouâdThe main purpose of this thesis is to study a class of mathematical models describing some problems related to the infection by the Plasmodium falciparum parasite which causes malaria and whose vector is the female mosquito of the species Anopheles. The work is divided into three main parts, the first part is related to the analysis of the spread of malaria in an isolated population. The global stability of the disease-free equilibrium is studied according to the different epidemiological parameters when the basic reproduction number is lower than one. When this number is higher than one, the existence of a unique endemic equilibrium is proved. Inspired by the geometric approach introduced by Li and Muldowney, we provided a sufficient condition for this endemic equilibrium to be globally asymptotically stable. A state estimator was constructed to estimate the size of human populations based on the measurement of the number of newly infected humans per unit time. We also proposed two control strategies to eradicate the disease. Finally, to better understand the dynamics of the spread of the disease and to identify the most influential parameters, we have studied the local sensitivity of the number of basic reproduction with respect to each parameter. The second part is about the study of a model that describes the interaction and the spread of the disease within a human population that is divided into two subpopulations, local and non-local. The first subpopulation follows a linear growth while the non-local population follows a logistic growth among the first. We choose to study the impact of the migration of people from an endemic country to another country declared free of the disease or towards the eradication of the disease. Our analysis yielded conditions of the persistence of the disease, we studied the possibility of controlling the disease in a first step through the control of the carrying capacity, then we developed a method based on a matrix called matrix of vectorial transmission which was used to determine the link between the two subpopulations and the population of mosquitoes, according to the values of this matrix entries in order to ensure the control of the disease spread. In addition, a local and global sensitivity study of the level of local and non-local infection was performed to determine the most influential model input parameters. The last part is devoted to the study of the global dynamics of models with multiple subpopulations that are assumed to be weakly interconnected. Our work highlights a process that allows us to perform a complete analysis of many dynamical systems modeling the spread of a disease that involves different populations. The objective is to be able to determine the global stability of the disease-free equilibrium when the basic reproduction number is less than one as well as the global stability of the different types (interior or frontier) of endemic equilibria as a function of the different local basic reproduction numbers and the nature of the interconnections between the network components.Item Etude Spectrale de Matrices de Covariance d′un Processus Autorégressif AR.(university of tlemcen, 2021-10-23) Khettab, ZahiraThis thesis deals with the study of the limit spectral distribution of a class of large random matrices having correlated entries. We are interested in the asymptotic behavior of large covariance matrices whose entries are correlated by the relation of an autoregressive of order one. In this context, we show that the empirical eigenvalue distribution function of the covariance matrix converges almost surely to a non-random function given by Marcenko and Pastur. Our approach consists of a centralization and a truncation of strongly geometrically mixing random variables and an application of the Stieltjes transform method which makes it possible to obtain, under certain conditions, the integral equation of the limit spectral distribution, and we thus show a universality result concerning the asymptotic behavior of the spectrum of these covariance matrices. We also investigate the case of matrices whose columns are autoregressive processes of order one. This extends on the one hand the Örst result to a vector framework and on the other hand generalizes the results on matrices with independent identically distributed entries. Finally, we present numerical simulations illustrating the behavior of the estimator of the spectral density of the matrices in question around the true density by varying the various parameters.Item Propriétés spectrales de certains générateurs infinitésimaux dans un espace de Fréchet de type hyperbolique(University of Tlemccen, 2021-07-14) Cherrifi Amina, HadjiatItem Application de la théorie des Équations Différentielles Abstraites (EDA) à des problèmes de dynamique de population(10-05-2022, 2022-03-30) Dib-Baghdadli, Nabahats AdibaIn this thesis, we consider the infestation of a village by the domestic species Triatoma. Dimidiata. The village adjoins a forest representing the habitat of vectors. The latter go to the village to eat. Food is a meal of blood from the humans or mammals they breed. The transmission of Trypanosoma Cruzi from vector to host takes place mainly during this phase. In this work, we consider a triatomic population structured in time and space. The processes of demography and spatial dispersion are captured by reaction-diffusion equations in two-dimensional space. In adequate functional spaces, the system of partial differential equations is transformed into an abstract differential equation. Our first objective is to show that the operator generates an analytical semi-group. We then prove the existence and uniqueness of a local solution to the corresponding Cauchy problemItem Dérivations fractionnaires discrètes et applications numériques.(06-06-2021, 2020-02-29) Khitri Née Kazi Tani, LeilaThis thesis focuses on the construction of discrete fractional operators as fractional powers of sectorial operators. This approach requires the construction of resolvents and control of their norms in various Banach spaces. This original approach in the discrete case, allowed us to find some operators and to build a new one. Following this, essential convergence results are proved. We show the uniform convergence of the operator nabla h-sum to the Riemann-Liouville integral in the spaces of the continuous functions and then in weighted continuous spaces. Also, the strong convergence of fractional nabla operators to the fractional derivative operator in Hölder spaces is proved. As applications the resolution of some problems of fractional Cauchy is proposed.Item Sur une classe de problèmes elliptiques non locaux et non-linéaires avec terme singulier(08-04-2021, 2019-12-18) Dieb, AbdelrazekIn this thesis, we are interested in studying non-local semi linear elliptic problems with Dirichlet or Dirichlet-Neumann external boundary conditions. Our objective is to generalize the same type of existence and multiplicity results, known in the case of the Laplacian, in the case of the fractional Laplacian.Item Solvabilité d’une classe de problèmes non-linéaires singuliers associés à des équations différentielles ordinaires(08-04-2021, 2020-09-29) Kerris -Boukli Hacene, SouhilaDans cette thËse, nous avons appliquÈ une approche variationnelle pour líÈtude de certains problËmes aux limites pÈriodiques associÈs ‡ des Èquations di§erentielles (systËmes díÈquations di§erentielles) du second ordre sous líe§et díimpulsions Nous avons ÈtÈ essentiellement concernÈs par líÈtude de líexistence de solutions periodique au voisinage de solutions constantes et par líÈtude de líexistence de solutions homoclinique et heteroclinique pour des equations di§erentielles et des systËmes couplÈs dans le cas de perte de rÈgularitÈ (singularitÈ) et sous líe§et díimpulsions (cf. [34], [35] et [36]) Les rÈsultats ont ÈtÈ Ètablis par minimisation sous contraintes en considÈrant des conditions su¢ santes assez simples.Ces rÈsultats ont fait líobjet de deux publications (1)N. Daoudi-Merzagui, S. Kerris ,Homoclinic solutions for singular impulsive second order di§erential equations , Applied Mathematical Sciences, Vol. 11, 2017, no. 24, 1187-1210 https://doi.org/10.12988/ams.2017.74120 (2)N. Daoudi-Merzagui, S. Kerris, Variational Approach to a Singular Damped Second-Order Systems under Impulses E§ects, Afrika Matem